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Cardinal interpolation, submodules and the 4-direction mesh

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Abstract

This paper introduces the idea of cardinal interpolation on submodules of Zd by translates of box splines if the condition of global linear independence fails to hold. In particular, the special case of the 4-direction box splines is discussed, where the pertinent submodule is given by the pairs (k, l) of integersk, l withk+l even. For this case, one obtains results that parallel the known results for the 3-direction box splines.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Duisburg, 4100, Duisburg, F.R.G.

    Kurt Jetter

  2. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada

    Sherman Riemenschneider

Authors
  1. Kurt Jetter
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  2. Sherman Riemenschneider
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Communicated by Klaus Höllig.

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Jetter, K., Riemenschneider, S. Cardinal interpolation, submodules and the 4-direction mesh. Constr. Approx 3, 169–188 (1987). https://doi.org/10.1007/BF01890562

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  • DOI: https://doi.org/10.1007/BF01890562

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